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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 29232.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29232.i1 | 29232bn2 | \([0, 0, 0, -23511, -1052494]\) | \(7701397204048/1892605743\) | \(353205654181632\) | \([2]\) | \(110592\) | \(1.5020\) | |
29232.i2 | 29232bn1 | \([0, 0, 0, -8076, 265655]\) | \(4994190819328/276357501\) | \(3223433891664\) | \([2]\) | \(55296\) | \(1.1555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29232.i have rank \(0\).
Complex multiplication
The elliptic curves in class 29232.i do not have complex multiplication.Modular form 29232.2.a.i
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.